For years, the problem of tracking and disturbance suppressing of a repetitive signal has been attracting much attention in the art. Repetitive control based on internal model principle is an effective control method for this purpose. FIG. 1 shows the structure of a control system having a conventional repetitive controller. As shown in FIG. 1, the given input quantity of the control system is denoted by r, and the output quantity of the control system is denoted by y. The control error quantity r−y of the control system is input into a repetitive controller 100 as its input quantity denoted by e. The repetitive controller 100 includes an internal model section 1, a periodic delay module 2, and a compensation module 3 which are connected in series. The input quantity e is input via the input terminal of the internal model section 1. The internal model section 1 makes the fundamental wave distortion occurred in the last period to be reproduced in the next period. The signal output from the internal model section 1 is subjected to the following periodic delay and compensation to obtain a repetitive-controlled output control quantity ur. Then the control quantity u, is applied to the controlled object P(z). The disturbance d is superposed on the signal output from P(z) to obtain the output quantity y of the control system.
The internal model section 1 is a critical unit in the repetitive controller 100. It is a closed loop system consisting of a forward path, a feedback path and an adder. The feedback path includes an internal model periodic delay module z−N and an internal model filter module Q(z) which are connected in series. The transfer function of an ideal internal model (Q(z)=1) is as follows:
            z              -        N                    1      -              z                  -          N                      ,The extreme point of the above transfer function is kω0, where k is an integer and ω0 is the fundamental wave angular frequency. As can be seen, the gain of the ideal internal model on the fundamental wave and the integer harmonics is infinite. Since the input quantity e=r−y, the harmonic components in the input quantity e are in reverse direction to that of the harmonic components (i.e. the disturbance d) in the feedback quantity y. Thus, after the disturbance d is superposed, those harmonic components may counteract with each other and the finally obtained feedback quantity y does not contain any integer harmonics. As can be seen, in the above control system the integer harmonic components may be cancelled. That is, all the integer harmonic components can be removed.
However, in actual electric and electronic systems, only harmonics at some particular frequencies need to be tracked or cancelled. For example, the harmonic components resulted from dead time effect and non-linear load mainly include the 3rd, 5th, and 7th harmonic components, but include very few harmonics of medium and high frequencies. In such cases, if the above described conventional repetitive controller is used, the large gain of the conventional repetitive controller at medium and high frequencies may cause the stability margin of the whole control system to be reduced, such that the control performance requirements of the system can not be met. In view of this, it is desired to propose a novel repetitive controller which only cancels the harmonics at particular frequencies so that the control performance of harmonic canceling may be performed with respect to the particular frequencies and the stability margin of the whole control system may be improved.